What are you planning to grow? Do you want to fence the dogs in or out? What varmints live in your area that you might also want to fence out of your garden?

If the dogs are all you are worried about then chain link (aka Cyclone) fencing works very well. Won't do much to keep all the other garden varmints out but very effective for dogs and attractive.

Not sure what you mean about "leech chemicals in to the soil" as I can't think of any form of common fencing that would do that.

Dave

Here is a link that might be useful: All kinds of garden fence photos for ideas

The Potager forum isn't very active right now, but if you're looking for pretty yards, look there or else the Cottage garden forum!
None of us seem quite clear what you're looking for, so you might be a little more clear? Decorative, dog proof, functional, pretty?
How big/long are we talking about? Do you just want the dogs to stay out of the orchard? Do you want the garden fenced off from the yard and orchard?
AND....the big question is how much do you have to pay for these fences?????? Personally, I wouldn't pay a bunch for a decorative fence to keep a dog out of a garden, but I would try to make a fence/gate pretty to go into a pottager/type garden.
You can also grow pretty stuff on a functional fence! If it is away from your vege garden and just keeping the dogs out, you can grow Morning Glories or many kinds of vines to make an ugly fence beautiful! (Just keep those invasive things like Morning Glories and Nasturtiums out of the vege garden proper!)
Just a few thoughts! Nancy

There are a lot of options . Depend on how much budget you have. If it is strictly for the purpose of keeping the dogs out, a simple chicken fence net can do. Cheaper plastic ones are also other option but might not be good under Arizona hot sun.. If you know some simple wood working and have a table saw, you can make nice picket fence ( 3' tall)with 5/8" thick cedar lumber. The come in 5/8" - 5 1/2" by 6'. @ about $1.50 each. You can make 4 piece of each. Again, it depends how big a garden area there is involved. Since you have dogs, probably wont have visitors like rabbits. or deer. LOL

Thank you all! Sorry I wasn't more descriptive about what I need. We don't have critters here to worry about. Just these dogs! I know they will destroy all of our hard work! I want them fenced out of the area. We basically converted a large area of our yard for a big veggie garden and several different fruit trees. It's 22' x 29' and I want it to look nice when fenced since it's a focal point in the yard. The dogs are on the smaller side so it probably doesn't need to be more than 3' high. Cost is somewhat of an issue but not the #1 deciding factor. Thanks for all you have given me, I'm going to start looking at your suggestions now.

I recommend something like the one shown below, about 3 ft high. Natural cedar or painted green or white. You will need about 100 running feet of it plus a gate. Material cost of it may be about $200, if you make it yourself.

Very nice fence! I was going to post the potager from Practical Magic, which is very similar...here it is :)
{{gwi:10430}}From Lavender Lass farmhouse pictures

If you want to go an easy-peasy route, home depot sells fence panels that are all assembled and you have to do is come up with a way to put them up. Lots of different styles, but you will definitely pay a premium for them, cost of convenience and all.

My dogs dig voles that like the soil among the mature apple and pear trees, which makes a mess but is of certain benefit.

In the veg garden I use temporary chicken wire fences to keep dogs, cats and chickens off of sensitive beds.

One suggestion: Don't try to alter the current dog trails through your yard too much. Instead try to design around them, within reason.